Question

The length of two open organ pipes are l and $(l + \Delta l)$ respectively. Neglecting end correction, the frequency of beats between them will be approximately

• A. $\frac{v}{2l}$
• B. $\frac{v}{4l}$
• C. $\frac{v\Delta l}{2l^{2}}$
• D. $\frac{v\Delta l}{l}$ (Here v is the speed of sound)

Answer 1

Answer: (C)

$\frac{v\Delta l}{2l^{2}}$

Answer 2

$\lambda_{1} = 2l,\lambda_{2} = 2l + 2\Delta l$⇒ $n_{1} = \frac{v}{2l}$ and $n_{2} = \frac{v}{2l + 2\Delta l}$

⇒ No. of beats

$= n_{1} - n_{2} = \frac{v}{2}\left( \frac{1}{l} - \frac{1}{l + \Delta l} \right) = \frac{v\Delta l}{2l^{2}}$